Least Common Multiple (LCM) of 84 and 23
The least common multiple (LCM) of 84 and 23 is 1932.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 84 and 23?
First, calculate the GCD of 84 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 23 = 3 remainder 15 |
| 2 | 23 ÷ 15 = 1 remainder 8 |
| 3 | 15 ÷ 8 = 1 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 99 | 7326 |
| 135 and 160 | 4320 |
| 192 and 40 | 960 |
| 42 and 178 | 3738 |
| 49 and 80 | 3920 |